Stochastic dynamical models described by Fokker-Planck equations, in the limit of weak noise, can be formally associated with Hamiltonian dynamical systems. Of special interest are “Fokker-Planck Hamiltonians” with a certain smooth separatrix at zero energy, since a differentiable macroscopic potential was shown to exist in this case. In this article we will construct integrable Fokker-Planck Hamiltonian system with the help of the method developed by Yehia [3]. The research resulted nine integrable systems of which eight are new and one repeats a known case due to Hietarinta [12]. An example is given to illustrate the use of the new systems in constructing steady state solution for certain Fokker-Planck equations.

Fokker-Planck equation, polynomial integral-stochastic dynamical system.